EFFECTIVE ODDS
When there is only one round of betting left and only one card to come, comparing your chances of improving to the pot odds you are getting is a relatively straightforward proposition.
If your chances of making a hand you know will win are, say, 4to1 against and you must call a $20 bet for the chance to win a $120 pot, then clearly your hand is worth a call because you’re getting 6to1 odds the pot is offering you (excluding bets on the end) are greater than the 4to1 odds against you making your online poker hand.
However, when there is more than one card to come, you must be very careful in determining your real pot odds.
Many players make a classic mistake: They know their chances of improving, let’s say, with three cards to come, they compare those chances to the pot odds they are getting right now.
But such a comparison is completely off the mark since the players are going to have to put more money into the pot in future betting rounds, and they must take that money into account.
It’s true that the chances of making a hand improve greatly when there are two or three cards to come, but the odds you are getting from the pot worsen.
REDUCING YOUR POT ODDS WITH MORETHAN ONE CARD TO CAME
Let’s say you are playing hold’em, and after the flop you have a fourflush that you are sure will win if you hit if. There are two cards to come, which improves your odds of making the flush to approximately 1¾to1.
It is a $10$20 game with $20 in the pot, and your single opponent has bet $10. You may say, “I’m getting 3to1 odds and my chances are 1¾to1.
So I should call.” However, the 1¾to1 odds of making the flush apply only if you intend to see not just the next card, but the last card as well, and to see the last card you will probably have to call not just $10 now but also $20 on the next round of betting.
Therefore, when you decide you’re going to see a hand that needs improvement all the way through to the end, you can’t say you are getting, as in this case, 30to10 odds.
You have to say, “Well, if I miss my hand, I lose $10 on this round of betting and $20 on the next round. In all, I lose $30.
If I make my hand, I will win the $30 in there now plus $20 on the next round for a total of $50.” All of a sudden, instead of 30to10, you’re getting only 50to30 odds, which reduces to 1²∕³to1.
These are your effective odds the real odds you are getting from the pot when you call a bet with more than one card to come.
Since you are getting only 1²∕³to1 by calling a $10 bet after the flop, and your chances of making the flush are 1¾to1, you would have to throw away the hand, because it has turned into a losing play that is, a play with negative expectations.
The only time it would be correct to play the hand in this situation is if you could count on your opponent to call a bet at the end, after your flush card hits.
Then your potential $50 win increases to $70, giving you 70to30 odds an justifying a call.(* While a call on the flop might be a bad play, a semibluff raise could be a good play. Sometimes folding is a better alternative to calling, but raising is the best alternative of all. (See Chapter Eleven and Thirteen.) backdoor flush draw in hold’em, and an opponent bets $10.)
With a backdoor flush you need two in a row of a suit. To make things simple, we’ll assume the chances of catching two consecutive of a particular suit are 1/5 X 1/5.
That’s not quite right, but it’s close enough.³ It means you’ll hit a flush once in 25 tries on average, making you a
24to1 underdog.(*For the finicky, the exact equation is 10/47 x 9/46. Ten of the 47 unseen cards make a fourflush on fourth street, and then nine of the 46 remaining cards will produce the flush at the end.)
By calling your opponent’s $10 bet, you would appear to be getting 26to1. So you might say, “OK, I’m getting
26to1, and it’s only 24to1 against me. Therefore, I should call to try to make my flush.”
Your calculations are incorrect because they do not take into account your effective odds. One out of 25 times you will win the $260 in there, plus probably another $40 on the last two rounds of betting.
Twenty times you will lose only $10 when your first card does not hit, and you need not call another bet. But the remaining four times you will lose a total of $30 each time when your first card hits, you call your opponent’s $20 bet, and your second card does not hit.
Thus, after 25 such hands, you figure to lose $320 ($200+$120) while winning $300 for a net loss of $20. Your effective poker odds reveal a call on the flop to be a play with negative expectation and hence incorrect.
